There's no distinct seasons in Singapore, and you are as likely to get sunny weather one day as a downpour on the next. the later months like Nov and Dec are a bit wetter though, while June and July are usually the drier months.
Even with this wet and wetter pattern, there is a degree of predictability. The rain tends to start mid or late afternoon. Always take an umbrella with you - good for rain and shade.
However, with the changes in climate the weather is becoming a little bit erratic. Water spouts have been seen in Singapore harbor. In December 2006 the monsoon moved from it's easter track to a path that took it over Singapore and parts of peninsular Malaysia - Johor Bahru had the worst flooding in 100 years.

